Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x, AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2. What is the value of x?

Question

Mathematics

Ashleigh Blackwell

2 December, 09:27

Triangle ABC and Triangle DEF are similar. For triangle ABC, AB = 2x, AC = 24 inches and BC = 20. For triangle DEF, EF = 5 and DF = x - 2. What is the value of x?

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Answers (1)

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George French · Answer 1

X=8.

Following the similarity statement, we know that AC is to DF as BC is to EF. The ratio would be:

24 / (x-2) = 20/5

Cross multiply:

24*5 = 20 (x-2)

Use the distributive property:

120 = 20x - 40

Add 40 to both sides:

120+40 = 20x - 40 + 40

160 = 20x

Divide both sides by 20:

160/20 = 20x/20

8 = x